Retroreflective cube corner articles are known. Such articles incorporate cube corner elements, each such cube corner having three approximately mutually perpendicular facets of high reflectivity. The reflective facets interact with light to cause each cube corner element to redirect incident light back in the general direction from which it originated, regardless of the angle of incidence of the light. This functionality is useful in applications requiring enhanced visibility, e.g. street and highway signs, traffic control barrels and cones for placement in and along roadways, and vests or other articles of clothing for persons who engage in work or other activities around nighttime traffic. The reflectivity of the facets may be provided by total internal reflection, or by a layer of metal or other reflective material coated onto the facet. It is also known to design the cube corners so that the dihedral angles between the three reflective facets deviate slightly from perfect perpendicularity, so that the retroreflected light deviates slightly from the direction of the incident light. In this way, more of the retroreflected light is likely to be seen by a person whose eye subtends a small but nonzero angle relative to the direction of the incident light. Reference in this regard is made to U.S. Pat. No. 4,775,219 (Appeldorn et al.).
It is known for a given cube corner article to be fabricated using a tool having a structured surface. The structured surface of the cube corner article may be made by microreplication from the structured surface of the tool. The structured surface of the tool is thus an inverted version or negative replica of the structured surface of the given cube corner article. As such, the tool also includes groups of three approximately mutually perpendicular facets, and whether or not the tool itself provides any retroreflectivity of light, it can be considered to be a cube corner article.
It is also known to provide cube corner articles with a tiled configuration, in which distinct cube corner arrays are arranged in a pattern of adjacent regions or zones, referred to herein as tiles. The tiling typically modifies the entrance and orientation performance of the article. Commercially available retroreflective cube corner sheeting uses tiles having, in plan view, the shape of long strips or rectangular areas (inclusive of squares), a minimum characteristic dimension of which is on the order of 0.150 inches (3.8 mm) or more. The orientation of cube corner elements is different between any two adjacent tiles.
Three known retroreflective cube corner articles that employ tiling will now be discussed. FIGS. 1, 1A, and 1B relate to a tiled retroreflective article discussed in U.S. Pat. No. 5,936,770 (Nestegard et al.). FIG. 1 depicts a magnified view of a portion of the structured surface of a retroreflective cube corner sheeting 110 which is designed to exhibit improved retroreflective performance at high entrance angles in exactly two primary planes, and to exhibit substantially similar retroreflective performance at varying entrance angles in each of the two primary planes. The structured surface includes a plurality of alternating zones which comprise an array of cube corner elements 112. The cube corner elements 112 are disposed as optically opposing matched pairs in an array on one side of the sheeting. Each cube corner element 112 has the shape of a trihedral prism with three exposed planar faces 122. The dihedral angle between the faces 122 is about 90°, but can deviate slightly from 90° as discussed in the '219 Appeldorn patent. The cube corner elements 112 preferably have a canted geometry as disclosed in U.S. Pat. No. 4,588,258 (Hoopman). Such canting defines a single primary plane of improved retroreflective performance at high entrance angles and a single secondary plane of improved retroreflective performance at high entrance angles. The axes of the cube corner elements can be canted in a “backward” or “negative” direction as discussed in U.S. Pat. No. 5,565,151 (Nilsen), or in a “forward” or “positive” direction as discussed in the '258 Hoopman patent.
The structured surface of the sheeting 110 includes a plurality of alternating zones (“tiles”) of cube corner arrays disposed at approximately ninety degree orientations. Sheeting 110 may thus be characterized in that it includes a first zone 106 including an array of cube corner elements disposed in a first orientation on the sheeting and a second zone 108 of cube corner elements disposed in a second orientation on the sheeting to define a first primary plane of improved retroreflective performance at high entrance angles and a second primary plane of improved retroreflective performance at high entrance angles which is perpendicular to the first plane.
The first zone 106 extends substantially parallel with a longitudinal edge of sheeting 110. The first zone 106 includes an array of cube corner elements 112 formed by three mutually intersecting sets of grooves including two secondary groove sets 126, 128, and a primary groove set 130. The individual cube corner elements 112 in the array are formed such that their optical axes are canted in a plane perpendicular to the primary groove 130. The cube corner array in first zone 106 thus exhibits a primary plane of improved retroreflective performance which extends perpendicular to the primary groove 130, and perpendicular to the longitudinal edge of the sheeting 110. The individual cube corner elements are canted through an angle of approximately 8.15 degrees with respect to an axis normal to the base of the cube corner element to define base triangle included angles of 55.5 degrees, 55.5 degrees, and 69 degrees. The second zone 108 extends substantially parallel to the first zone 106 along the length of the sheeting, and includes an array of cube corner elements 112 substantially identical to the array disposed in the first zone 106, except that the array in the second zone is disposed at a ninety degree orientation relative to the array in first zone 106. It is said that advantages may be obtained by canting opposing cube corner elements through an angle between about 7 degrees and about 15 degrees (see e.g. the '258 Hoopman patent), but that varying degrees of canting and varying cube sizes can be used.
FIG. 1A depicts the retroreflective characteristics of a single cube corner array in accordance with the '258 Hoopman patent. Such a cube corner array exhibits a single principal plane which exhibits improved retroreflective performance at high entrance angles, represented by the plane extending through the two broadest lobes of the isobrightness contours, and a secondary plane, which exhibits improved retroreflective performance at high entrance angles, represented by the plane which extends through the two shorter lobes of the isobrightness contours. Accordingly, sheeting manufactured to have such a single cube corner array has a single preferred orientation. The embodiment of FIG. 1 is said to overcome this limitation by providing two planes which exhibit improved retroreflective performance at high entrance angles. As disclosed in PCT Publication WO 96/42025 (Smith et al.), backward canted cubes may be configured (e.g., base angles of 50°, 65°, 65°) to have two similar preferred planes of entrance angularity. The two preferred planes of entrance angularity are not necessarily perpendicular to each other.
FIG. 1B is an isobrightness contour graph of retroreflective brightness readings taken from a sample of dual orientation sheeting in accordance with FIG. 1. A description of retroreflective testing geometries and measurement angles is supplied in ASTM E-808-93b, Standard Practice for Describing Retroreflection (a more current version of which is designated ASTM-E-808-01 (2009)), and pertinent angles and other geometrical factors are also discussed below in connection with FIG. 4. The measurements of FIG. 1B were taken at a fixed observation angle of 0.33 degrees and a fixed presentation angle of 90 degrees. The entrance angle was varied between 0 and 80 degrees and the sheeting was rotated through a 360 degree range of orientation angles. In FIG. 1B, entrance angles are represented by concentric circles, while orientation angles are represented by numerals extending radially around the graph. The concentric isobrightness contours represent the relative retroreflectance of the retroreflected light; the maximum retroreflectance is represented by the center point on the graph and concentric isobrightness contours representing five percent reductions in retroreflectance relative to the maximum, measured in candelas/lux/meter2.
Referring to FIG. 1B, the retroreflective sheeting of FIG. 1 exhibits exactly four broad lobes of improved retroreflective performance at high entrance angles. These four lobes occur at 90 degree intervals beginning at a zero degree orientation angle (e.g. at 0, 90, 180, and 270 degrees orientation angle). These four lobes define two primary planes of improved retroreflective performance at high entrance angles: the first plane extends through the plane of the sheeting at a 0-180 orientation and the second plane extends through the sheeting at a 90-270 orientation. The sheeting is also said to exhibit substantially similar retroreflective performance across varying entrance angles within these two planes. In use, the sheeting may be oriented in either of two different orientations to enable the sheeting to provide optimal retroreflective performance.
For further design details and variations of retroreflective articles such as that of FIG. 1, the reader is directed to the '770 Nestegard patent.
FIG. 2 is a schematic plan view of another cube corner retroreflective sheeting 270 that employs tiling. The tiled sheeting 270 was sold in commerce by the Stimsonite Corporation of Niles, Ill., under the trade name STIMSONITE High Performance Grade Reflective Sheeting (Lot 1203W, Product Number 8432170). The tiled sheeting 270 employs a plurality of tiled arrays of backward canted cube corner element matched pairs. The structured surface of the sheeting 270 includes a plurality of groups of cube corner element matched pair arrays positioned at a plurality of distinct orientations relative to a longitudinal edge 272 of the sheeting 270. The cube corner arrays are oriented such that the primary grooves of the arrays lie in planes that are positioned at orientations of 0 degrees, 30 degrees, 60 degrees, and 90 degrees relative to longitudinal edge 272 of sheet 270.
For further details of the tiled sheeting 270, as well as descriptions of other tiled retroreflective articles, the reader is directed to U.S. Pat. No. 5,822,121 (Smith et al.).
FIG. 3 is a tiled cube corner article 310 discussed in patent application publication US 2011/0013281 (Mimura et al.). The cube corner article 310 has a structured surface in which facets thereof form first cube corner arrays 313-1 and second cube corner arrays 313-2 arranged into alternating strip tiles 312-1, 312-2, respectively. The structured surface defines a reference plane, shown as the x-y plane of a Cartesian x-y-z coordinate system. The first cube corner arrays 313-1 have cube corners 314-1 and 315-1. These cube corners are canted. That is, the optical axis (sometimes referred to as the symmetry axis) of each cube corner is tilted with respect to the normal axis of the plane, i.e., with respect to the z-axis. The second cube corner arrays 313-2 have cube corners 314-2 and 315-2, which are also canted. The projections of the optical axes of the various cube corners on the x-y plane are shown in the figure as optical axes 314d-1, 315d-1, 314d-2, and 315d-2 for the cube corners 314-1, 315-1, 314-2, 315-2, respectively.
The Mimura reference describes an embodiment in which cube corners 314-1 and 315-1 have base triangles whose ordered interior angles or base angles are (54.918°, 66.659°, 58.423°), and in which cube corners 314-2 and 315-2 have base triangles whose ordered interior angles are (54.918°, 58.423°, 66.659°). Further discussion of base triangles and their ordered angles is provided below. A given one of the cube corners 314-1 and an adjacent one of the cube corners 315-1 form a matched pair of cube corners, because the cube corner 314-1, if rotated 180 degrees about the z-axis, produces a cube corner that has the same cube geometry and the same cube orientation as the cube corner 315-1. A given one of the cube corners 314-2 and an adjacent one of the cube corners 315-2 also form a matched pair of cube corners, for the same reason. However, any given cube corner within the array 313-1 does not have the same cube geometry as, and does not form a matched pair with, any cube corner within the array 313-2.